When we’re taught about vibrations, every mathematical modelisation deals with a system of a fixed spring whose end has a certain mass, but how does this relate to real-world systems like a bridge or a building? The natural frequency of the spring-mass system is the number of back-and-forth movements being done per second, but what’s the equivalent of that for let’s say a building or a bridge or any real-life application?
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Not a direct answer to your question but just a note on why the spring-Mass model is so important in physics:
The Mass on a spring is an example of a system where the force on the mass is lineair with the displacement. If you move the mass 10cm from it’s equilibrium the force is twice as big as when you move it only 5cm. It’s often the first example you see because it’s eassy to vizualize and do experiments with.
There are accually a lot of systems that behave in the same way when they are displaced by a small amount around their equilibrium.
For example: the forces between atoms in a solid material. The full version of these forces is a very difficult equation. But we know an equilibrium: when the atoms follow the lattice perfectly. In most solids at room temperature the atoms will be very close to this equilibrium and models that simplify the forces to be lineair give good, predictive results.
For real life examples in bridgers or buildings I hope some engineers will react, but I’m certain they have many.
When we’re taught about vibrations, every mathematical modelisation deals with a system of a fixed spring whose end has a certain mass, but how does this relate to real-world systems like a bridge or a building? The natural frequency of the spring-mass system is the number of back-and-forth movements being done per second, but what’s the equivalent of that for let’s say a building or a bridge or any real-life application?
In: 0
Not a direct answer to your question but just a note on why the spring-Mass model is so important in physics:
The Mass on a spring is an example of a system where the force on the mass is lineair with the displacement. If you move the mass 10cm from it’s equilibrium the force is twice as big as when you move it only 5cm. It’s often the first example you see because it’s eassy to vizualize and do experiments with.
There are accually a lot of systems that behave in the same way when they are displaced by a small amount around their equilibrium.
For example: the forces between atoms in a solid material. The full version of these forces is a very difficult equation. But we know an equilibrium: when the atoms follow the lattice perfectly. In most solids at room temperature the atoms will be very close to this equilibrium and models that simplify the forces to be lineair give good, predictive results.
For real life examples in bridgers or buildings I hope some engineers will react, but I’m certain they have many.
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